Answer:
When we apply our temporal understanding to eternal states of being, we tend to be troubled by the idea of a party in heaven when there's horror going on simultaneously in hell.
But this objection puts a lot of power into the hands of people who have chosen to become, essentially, non persons. Keep in mind, that while Jesus said hell is filled with people in the torment of regret, it is more so filled with people who have volitionally sacrificed their personhood to cling to their own way, when LIFE was put before them (John 3:16-19). Why should the righteous be saddened for eternity by the outworking of God's goodness and justice?
Read CS Lewis' short novel, The Great Divorce to understand how we could find solace, not embarrassment or annoyance in God’s judgment. There is a great line in this book about this misconception that we could not enjoy heaven while hell was a reality. A heavenly creature asks, "how long will joy be held hostage by those who would deny it for themselves?" It’s a great parable about this whole problem.
That we think compassionate people should be troubled by hell for eternity shows a weakness in our understanding of both hell and compassion, not in God's actual plan to erect an eternal boundary between the righteous and unrighteous. How would you look at the man who has many houseguests, but who keeps his old reprobate, drunkard Uncle with them? Is that compassion? Who is it compassion on? The guests? Certainly not. His drunk uncle will try to rob them, molest them, and draw resources from them into his bottomless pit of selfish need. Is it compassion on the Uncle? No, because he doesn't want to be there, in their shared life and happiness. He's miserable and would rather be left alone.
It's true compassion then, just to give him what he wants.
You ask, why not just destroy them? What if they cannot be destroyed by the nature of how God made them? But why have their punishment go on? Yet, what if, in eternity, we don't mark time on a clock, what if eternity is not temporal and is just experienced as "now" and they don't really count years and months, as we probably also won't in heaven? Then the idea of spending "centuries" in hell is nonsense.
Also, the described tortures of hell are probably non literal, because if taken literally some are mutually contradictory. Hell is said to be dark AND a place of fire. Hell is a place of weeping AND gnashing of teeth. Hell is a pit AND a lake. The point behind the metaphors then, is to describe an existence of punishment, exclusion, and destruction. That's it. What that all means we don’t understand exactly, but we do understand the point: we don’t want to go there.
Thankfully we don’t have to. A way has been made to get right with God. A way that cannot be earned, but is offered to any who will receive Christ (John 1:12). He offers us his righteousness (a fitness for restored relationship with God) as a gift through Jesus’ sacrifice. So now you have a choice.
Before you get too wrapped up in how you’ll feel about another’s choice, God has always said to each individual, and says now specifically to you, “choose life” (Deut 30:19). Jesus might say to you what he said to Peter, when Peter asked about the fate of another: “what is that to you? You must follow me.”
